One option to consider could be AI. They have these hopping tourist flights which operate solely to allow tourists to cover various circuits.
One such is DEL-JAI-JDH-UDR-BOM and vv operating with an A319. The other is DEL-VNS-HJR-DEL operating with a A320.
With a 7 day visit India pass, you can do DEL-VNS on day 1, spend a day or 2 there, then take VNS-HJR on day 2 and HJR-DEL on day 3. Similarly for JAI-JDH-UDR circuit.
In typical AI fashion, these cant be purchased online: your TA will have to do it. I have friends in france who bought this Visit India passes on AI from the Eurail booking office.